"Mother and baby are doing beautifully," publicist Annett Wolf said. "They are really happy and everything is really good."
Messing gave birth to the couple's 5 pound 14 ounce son at a Los Angeles hospital Wednesday night. The couple have not yet picked a name for their, adding: "sometimes you need to see the baby first."
Wolf also told Reuters that Messing--who missed the final four episodes of Will & Grace when her doctor ordered her last month to stay off her feet for the rest of her pregnancy--was expected to return to the hit NBC comedy next season.
"This won't affect the schedule at all," Wolf said. "She will return to work in the summer as she has every year."